# Doppler Effect & Time Dilation: Explained

• Amr Elsayed
In summary, according to Janus, the combined effect of the Doppler shift and time dilation is that the wave speed is increased when the source is receding and decreased when approaching.
Amr Elsayed
Hi,
If I'm moving away from a light source flashing light, according to Doppler effect I would have more time between flashes from my perspective than a still observer from perspective of the source, my explanation would be that the source really waits this exact time, and I can relate it to a clock fixed on the source . According to the source it's flashing every 3 sec for instance on the fixed clock, and it's same for me and since I would feel that this moving clock " from my perspective is dilating " then I will have more time between flashes
What if I am moving toward the source emitting light ?? I want to use same clock but according to time dilation I should receive flashes and estimate time between them more than a person by the source will estimate time between emitting which is 3 sec on his clock , but Doppler effect is said to make time less not more ! that's where I get confused.

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What you are seeing in this situation can't be interpreted as a pure Doppler shift or a pure time dilation. Both things are going on.

Stephanus
bcrowell said:
What you are seeing in this situation can't be interpreted as a pure Doppler shift or a pure time dilation. Both things are going on.
Both are going on, but of course they can't oppose each other, so I'm sure I have a misunderstanding concerning time dilation with rate of emission when we are moving toward source of emission.

Amr Elsayed said:
Both are going on, but of course they can't oppose each other

Why not?

jtbell said:
Why not?
Because they simply lead to different consequences, I only get one
According to Doppler effect on rate of emission when I moving toward the source is increasing, more than the rate for a still body from perspective of source. But according to my understanding of time dilation of the fixed clock " which I think is wrong about that point" I should see the rate of emission decreasing , less than the still observer does. The problem is mainly about the clocks since I would relate emission to a specific time on clock

Amr Elsayed said:
Both are going on, but of course they can't oppose each other, so I'm sure I have a misunderstanding concerning time dilation with rate of emission when we are moving toward source of emission.

The Doppler shift component can be expressed as
$$F = \frac{1}{1+\frac{v}{c}} F_o$$

.

Using the same convention, the time dilation component follows the expression

$$\sqrt{1-\frac{v^2}{c^2}}$$

Combining the two gives you

$$F = \frac{\sqrt{1-\frac{v^2}{c^2}}}{1+\frac{v}{c}} F_o$$

which reduces to

$$F = \sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}} F_o$$

Where v is positive when the source is receding and negative when approaching.

Stephanus and Amr Elsayed
Amr Elsayed said:
Hi,Doppler effect is said to make time less not more ! that's where I get confused.
The confusion stems perhaps from the concept "relativistic Doppler", which includes time dilation. However the Doppler effect (without "relativistic" added) does not do anything with time.
Amr Elsayed said:
[..] I'm sure I have a misunderstanding concerning time dilation with rate of emission when we are moving toward source of emission.
From the perspective that you are moving, it is your clock that appears to be slow. On top of that there is a Doppler equation that fits the fact that you are moving towards a stationary source. Not only is time dilation opposite from the perspective that you are in rest and the source is moving, also the Doppler effect is slightly different. See this simple* explanation of the Doppler effect with throwing balls: https://en.wikipedia.org/wiki/Doppler_effect#Analysis

Janus presented here the derivation of the combined effect from the perspective that the source is moving and you are in rest.

Note: the combined effect ("relativistic Doppler) is the same from the perspective that you are moving, as it must be in view of the relativity principle.

* That illustration is great to make the effect understandable, but the picture of throwing balls does not match the fact that wave speed is independent of the speed of the source.

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Amr Elsayed
Re Janus's #6, I think there's a definitional problem with trying to split the relativistic Doppler effect into two numerical factors, one representing a nonrelativistic Doppler shift and one representing time dilation. In the nonrelativistic Doppler effect, we have three frames of reference: (1) the frame of the emitter, (2) the frame of the medium, and (3) the frame of the receiver. Any expression for the nonrelativistic Doppler effect implicitly refers to all three of these. But in the relativistic Doppler shift, there is no medium, so it's not possible to correctly associate the quantities appearing in the nonrelativistic formula with anything that actually exists.

I have a presentation of this kind of thing in more detail in my SR book, http://www.lightandmatter.com/sr/ . Section 3.1 uses spacetime diagrams and minimal math, and section 6.5 does it in fancier mathematical garb using the frequency four-vector.

Stephanus and Amr Elsayed
harrylin said:
The confusion stems perhaps from the concept "relativistic Doppler", which includes time dilation. However the Doppler effect (without "relativistic" added) does not do anything with time.
Janus said:
The Doppler shift component can be expressed as
F=11+vcFo​
F = \frac{1}{1+\frac{v}{c}} F_o

bcrowell said:
I think there's a definitional problem with trying to split the relativistic Doppler effect into two numerical factors, one representing a nonrelativistic Doppler shift and one representing time dilation.
yes, that's the case. I now get it, but I still need one more push to be okay,
If I am moving towards the source emitting light, according to the source, the moving body receives the light at a bigger rate because it's moving towards it. We can relate time on the moving clock fixed on the moving body to receiving light pulse, both time dilation and the relative velocity will cause us to see the the rate of flashes reaching the moving body bigger, and we measure for example 2 seconds on the moving clock between receiving 2 pulses, From perspective of the moving body it should measure also 2 sec on its clock, and the other clock by the source appears to be slow from the perspective of the moving body. I don't get how the moving body will measure 2 sec on it's clock between pulses if we relate shooting light pulses to specific times on the other clock that appears to be slow when we are moving since the other clock appears slow. If the source measures 4 sec between shooting pulses. If I am on the moving body, how can I measure 2 sec on my clock between receiving 2 pulses and 4 sec on the other clock between shooting pulses and it's slower from my perspective. It has sth to do with simultaneity
Thanks

I understand that when I'm moving towards a source of light I will see the rate of receiving light by another body stationary according to the source will be smaller than my rate . But briefly I don't clearly get If I should measure a bigger than from my perspective than the stationary observer measures for him self receiving light from his perspective. Here the comparison is in 2 different frames

Below is a pair of space-time diagrams. These are just displacement-time graphs with the time axis pointing up the page (the grid is at 1s intervals) and the position axis across the page (the grid is at one light second intervals).

They both show an observer who is stationary in this frame (green line, always at the position x=0) receiving light pulses from a source (purple line) moving at 0.6c. The dots on each line mark when their clocks tick - the green dots occur every second, and the purple dots every 1.25 seconds due to time dilation. Light pulses (dotted orange lines) are sent every time the traveller's clock ticks.

In the left graph, the purple observer is moving away from the green observer. The green observer receives a pulse every two seconds.
In the right graph, the purple observer is moving towards the green observer. The green observer receives a pulse every half second.

One can explain why the Doppler factor is what it is by observing that the purple source emits a pulse every 1.25s (according to the green observer), but moves 0.75 light seconds in that time, so the flight time for each pulse changes by 0.75s compared to its predecessor. Pulses therefore arrive every (1.25+0.75)s or every (1.25-0.75)s.

But what does this look like to the moving observer? I've re-drawn the space-time diagrams switching to the frames where the purple observers are at rest. In these frames, the green observer is doing 0.6c away from or towards the emitter.

Again, in the left graph the observers are moving apart; in the right graph they are moving together. Again, you can see that the ticks on the moving observers' lines occur at 1.25s intervals, while the stationary observers' ticks occur every 1s. But in these frames, the period of time when the green observer's clock is ticking is longer than the purple observers; it either started early or finished late. In other words, the relativity of simultaneity comes into this as you suggested.

Does that help?

Ibix said:
Does that help?
This would greatly help ! I didn't read the whole post because I think I concluded my problem from the first part, So please tell me if I'm wrong with the following in order to re-read your post
I don't necessarily see the calculated time dilation with my eyes, because light takes time to travel and in that time the moving source" from my perspective" has changed its position when shooting the second pulse. But I'm sure that the moving clock is dilating . So in your diagrams I will see the 2 pulses with .5 between them, but they were shot with 1.25 seconds between them from my perspective however I don't see or experience the 1.25 seconds.
Thank you

bcrowell said:
Re Janus's #6, I think there's a definitional problem with trying to split the relativistic Doppler effect into two numerical factors, one representing a nonrelativistic Doppler shift and one representing time dilation. In the nonrelativistic Doppler effect, we have three frames of reference: (1) the frame of the emitter, (2) the frame of the medium, and (3) the frame of the receiver. Any expression for the nonrelativistic Doppler effect implicitly refers to all three of these. But in the relativistic Doppler shift, there is no medium, so it's not possible to correctly associate the quantities appearing in the nonrelativistic formula with anything that actually exists.

I have a presentation of this kind of thing in more detail in my SR book, http://www.lightandmatter.com/sr/ . Section 3.1 uses spacetime diagrams and minimal math, and section 6.5 does it in fancier mathematical garb using the frequency four-vector.
I don't see any problems with that. Janus's post is pretty standard, it's not a matter of "trying".The Doppler effect directly follows from the light postulate which is based on Maxwell's theory. In the relativistic approach a standard "rest" system corresponds exactly with the classical "ether frame" for the predicted Doppler effect according to the time reckoning of the "rest" system.

That's right.

Note that we're both assuming Einstein's definition of simultaneity here in order to assign times to events that happen away from us. It's a perfectly reasonable assumption, but formally, it's still an assumption.

Amr Elsayed
Amr Elsayed said:
I understand that when I'm moving towards a source of light I will see the rate of receiving light by another body stationary according to the source will be smaller than my rate . But briefly I don't clearly get If I should measure a bigger than from my perspective than the stationary observer measures for him self receiving light from his perspective. Here the comparison is in 2 different frames
Just a little check, two comments about the way you phrased your questions. I'm looking at the parts in bold face:

"I understand that when I'm moving towards a source of light I will see the rate of receiving light by another body stationary according to the source will be smaller than my rate . But briefly I don't clearly get If I should measure a bigger than from my perspective than the stationary observer measures for him self receiving light from his perspective".

1. The speed of light is independent of the speed of the source (I commented on that in the small print footnote of #7). For the speed of light, the motion of the source does not matter. Likely you understood that, but from the way you identified "stationary observer" with "stationary according to the source", I'm not sure.

2. Usually in discussions when we talk of "our frame" and "from our perspective", we mean that we measure with the assumption that we are in rest. But I think that you mean from the perspective that you are moving, and that makes your question a little unclear. Because when you measure the frequencies of pulses that you receive, you do that by comparing it with your clock. And your clock will be ticking slow from the perspective that you are moving. You can correct for that effect, just as you can correct for the effect that temperature has on your clock. Normally when people say that they "measured" something, it is what they got after making such corrections. It is not clear from your question if you corrected your clock reading to your perspective that you are moving.

Amr Elsayed
harrylin said:
Just a little check, two comments about the way you phrased your questions. I'm looking at the parts in bold face:
May be you didn't get all my points because of English writing, but concepts of " from our perspective , stationary observer" are clear for me. It's also clear that motion of the source affects frequency and wavelength ,but speed of the wave is the same.
But again, my English didn't seem to clearly represent my problem.You may not look at the next parts in future in bold face :) Now thanks for your help , and effort of you all. It's all clear now

Ibix said:
That's right.
Once more,thanks for the wonderful diagrams

harrylin

## 1. What is the Doppler Effect?

The Doppler Effect is a phenomenon observed in waves (such as sound or light) where the frequency of the waves appears to change when there is relative motion between the source of the waves and the observer. This results in a shift in the perceived wavelength and can be heard or seen as a change in pitch or color.

## 2. How does the Doppler Effect affect sound waves?

The Doppler Effect affects sound waves by changing the frequency and wavelength of the waves as the source of the sound moves towards or away from the observer. This causes a shift in the perceived pitch of the sound, with a higher pitch being heard when the source is moving towards the observer and a lower pitch when the source is moving away.

## 3. What is time dilation?

Time dilation is a phenomenon predicted by Einstein's theory of relativity where time appears to pass at different rates for objects in motion compared to those at rest. This means that time can appear to slow down or speed up depending on the relative velocity of the objects.

## 4. How does time dilation relate to the Doppler Effect?

Time dilation is closely related to the Doppler Effect because both are a result of relative motion between objects. The Doppler Effect affects the frequency and wavelength of waves, which can also impact the perception of time. In addition, time dilation is often observed in situations where the Doppler Effect is present, such as with objects moving at high speeds or in gravitational fields.

## 5. What are some practical applications of the Doppler Effect and time dilation?

The Doppler Effect and time dilation have numerous practical applications. One example is in medical imaging, where the Doppler Effect can be used to measure blood flow and velocity in the body. Time dilation is also used in global positioning systems (GPS) to account for the differences in time between satellites and receivers on Earth. Additionally, both phenomena are important in understanding the behavior of objects in space and can be used to study the properties of distant stars and galaxies.

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